In question 3 we're asked to submit the deadends of a given Kripke structure in DNF. I was given this FSM:
input: {a}
output: {}
init states: p&q
transitions: a&q&!p&!next(q)&next(p)|p&q&next(p)&next(q)|q&!a&!p&!next(p)&next(q)
State transition diagram:
![Given state transition diagram](https://q2a.cs.uni-kl.de/?qa=blob&qa_blobid=5051305281262529438)
Using the teaching tool I got the following Kripke structure of which I thought that only the states s0, s1, s4 and s5 are deadends as they don't have any outgoing transitions. When the exercise system displayed the solution as incorrect I thought that also s3 and s2 should be deadends because neither s2 nor s3 are init states and hence cannot be reached by any means.
![](https://q2a.cs.uni-kl.de/?qa=blob&qa_blobid=18384411604374994304)
As this also was displayed as incorrect it was obvious that the only possible solution can be s0, s1, s4, s5 and s3 being deadends but I don't get why exactly s3 is a deadend (and also why s3 and not s4 as well) as only the previous two solutions seem to make sense for me based on my understanding of deadends?